A letter explaining their attitude was collected earlier on Tuesday from the offices of lawyer Chris Venturas by the ZCU's chief executive Vincent Hogg.
Hogg declined to say what was in the letter and Venturas was not immediately available for comment.
Following an acrimonious meeting last Thursday between Hogg, ZCU chairman Peter Chingoka with three directors on the one hand and Streak, Venturas, batsman Grant Flower and bowler Andy Blignaut on the other, the ZCU refused to rescind its decision to depose Streak as captain and the players said they would provide their response on Tuesday.
That is now being studied by Chingoka, but it is not certain whether he will reveal its contents later in the day. A full board meeting might be called, an official said.
Sri Lanka arrive for a month's Test and One-day International tour on Saturday, with the first ODI set for next Tuesday in Bulawayo.
The selectors will therefore want to choose the Zimbabwe squad as soon as possible. Whether they include any of the 12 becomes the key question.